1. Fixing non-ll(1) grammars
COP4620 – Programming Language Translators Dr. Manuel E. Bermudez

2. Topics Problems with model grammar Fixing common prefices
Fixing left-recursion
New grammar: LL(1)

3. Model grammar Problems: → id := E; {id} SL is left recursive.
S → begin SL end {begin}
→ id := E; {id}
SL → SL S {begin,id}
→ S {begin,id}
E → E+T {(, id}
→ T {(, id}
T → P*T {(, id}
→ P {(, id}
P → (E) {(}
→ id {id}
Problems:
SL is left recursive.
E is left recursive.
T → P * T have common
→ P prefices.
Showing a grammar is not LL(1): easy.
PL grammars:
“mostly” LL(1).
This is our “model” PL grammar. We’ll
use it throughout Modules 07 and 08.

4. Fixing common prefices
Change: T → P * T { (, id }
→ P { (, id }
to: T → P X { (, id }
X → * T { * }
→ { +, ; , ) }
Follow(X)
⊇ Follow(T) due to T → P X
⊇ Follow(E) due to E → E+T , E → T
= { +, ;, ) } due to E → E+T, S → id := E ;
and P → (E)

5. Fixing common prefices
In general, change
A → 1
→ 2
. . .
→ n
to A →  X
X → 1
→ n
Hopefully all the ’s begin with different symbols.
If not, repeat !

6. Fixing left recursion of E
We have (…((( T + T) + T) + T)…)
Instead, we want (T) (+T) (+T) … (+T)
Change: E → E + T { (, id }
→ T { (, id }
To: E → T Y { (, id }
Y → + T Y { + }
→ { ; , ) }
Follow(Y)  Follow(E)
= { ; , ) }
Yikes: destroyed the left associatvity of ‘+’ !
Will fix this later.
No longer contains ‘+’:
we eliminated E → E + T

7. Fixing left recursion In general, Change: A → A1 A →  1 . . . . . .
→ An →  m
to: A → 1 X X → 1 X
→ m X → n X →
The ’s don’t begin with A.

8. Fixing left recursion of SL
We have (…(((S)S)S)…)
Instead, we want (S)(S) …(S)
Change: SL → SL S { begin, id }
→ S { begin, id }
To: SL → S Z { begin, id }
Z → S Z { begin, id }
→ { end }
Destroyed the left associatvity of ‘ ’.
Fixable, but won’t matter.

9. Modified grammar → id := E ; {id} SL → S Z {begin,id}
S → begin SL end {begin}
→ id := E ; {id}
SL → S Z {begin,id}
Z → S Z {begin,id}
→ {end}
E → T Y {(,id}
Y → + T Y {+}
→ {;,)}
T → P X {(,id}
X → * T {*}
→ {;,+,)}
P → (E) {(}
→ id {id}
Grammar is LL(1) !

10. summary Problems with model grammar Fixing common prefices
Fixing left-recursion
New grammar is LL(1)